A note on compact and σ-compact subsets of probability measures on metric spaces with an application to the distribution free newsvendor problem

This note identifies compact and σ-compact subsets of probability measures on a class of metric spaces with respect to the weak convergence topology. Moreover, it is shown by an example, that the space of probability measures on a σ-compact metric spaces not need to be σ-compact space, even though the converse statement holds true for metric spaces. The results are applied to an extended form of the distribution free newsvendor problem.